Generally, \(L_2\)  regularization effectively keeps the image generated from the moved latent code from being different from the original [1]}. In the StyleGAN latent space, we maintain the image similarity by minimizing the \(l_2\) - distance between \(w_a\)  and \(w_s\)  as follows:
\(\begin{aligned}\mathcal {L}_{\textnormal {reg}}=||w_a - w_s||_2.\end{aligned}\) 
